AutoMobile

CONTEXT: The purpose is to classify a given silhouette as one of three types of vehicle, using a set of features extracted from the silhouette. The vehicle may be viewed from one of many different angles.

DATA DESCRIPTION: The data contains features extracted from the silhouette of vehicles in different angles. Four "Corgie" model vehicles were used for the experiment: a double decker bus, Cheverolet van, Saab 9000 and an Opel Manta 400 cars. This particular combination of vehicles was chosen with the expectation that the bus, van and either one of the cars would be readily distinguishable, but it would be more difficult to distinguish between the cars.•All the features are numeric i.e. geometric features extracted from the silhouette

import pandas as pd
import numpy as np
import os
from sklearn.cluster import KMeans
from sklearn.preprocessing import LabelEncoder
from sklearn.preprocessing import MinMaxScaler
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
from sklearn.model_selection import GridSearchCV

%matplotlib inline

1. Import datasets

vehs = pd.read_csv('Part3 - vehicle.csv')

print(f"Shape: {vehs.shape}")

Shape: (846, 19)

vehs.head()

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
0	95	48.0	83.0	178.0	72.0	10	162.0	42.0	20.0	159	176.0	379.0	184.0	70.0	6.0	16.0	187.0	197	van
1	91	41.0	84.0	141.0	57.0	9	149.0	45.0	19.0	143	170.0	330.0	158.0	72.0	9.0	14.0	189.0	199	van
2	104	50.0	106.0	209.0	66.0	10	207.0	32.0	23.0	158	223.0	635.0	220.0	73.0	14.0	9.0	188.0	196	car
3	93	41.0	82.0	159.0	63.0	9	144.0	46.0	19.0	143	160.0	309.0	127.0	63.0	6.0	10.0	199.0	207	van
4	85	44.0	70.0	205.0	103.0	52	149.0	45.0	19.0	144	241.0	325.0	188.0	127.0	9.0	11.0	180.0	183	bus

vehs.dtypes

compactness                      int64
circularity                    float64
distance_circularity           float64
radius_ratio                   float64
pr.axis_aspect_ratio           float64
max.length_aspect_ratio          int64
scatter_ratio                  float64
elongatedness                  float64
pr.axis_rectangularity         float64
max.length_rectangularity        int64
scaled_variance                float64
scaled_variance.1              float64
scaled_radius_of_gyration      float64
scaled_radius_of_gyration.1    float64
skewness_about                 float64
skewness_about.1               float64
skewness_about.2               float64
hollows_ratio                    int64
class                           object
dtype: object

vehs['class'].unique()

array(['van', 'car', 'bus'], dtype=object)

There are no mistakes in tag names

vehs['class'].value_counts()

car    429
bus    218
van    199
Name: class, dtype: int64

Slightly imbalanced to have more car datapoints

EDA

vehs.describe()

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio
count	846.000000	841.000000	842.000000	840.000000	844.000000	846.000000	845.000000	845.000000	843.000000	846.000000	843.000000	844.000000	844.000000	842.000000	840.000000	845.000000	845.000000	846.000000
mean	93.678487	44.828775	82.110451	168.888095	61.678910	8.567376	168.901775	40.933728	20.582444	147.998818	188.631079	439.494076	174.709716	72.447743	6.364286	12.602367	188.919527	195.632388
std	8.234474	6.152172	15.778292	33.520198	7.891463	4.601217	33.214848	7.816186	2.592933	14.515652	31.411004	176.666903	32.584808	7.486190	4.920649	8.936081	6.155809	7.438797
min	73.000000	33.000000	40.000000	104.000000	47.000000	2.000000	112.000000	26.000000	17.000000	118.000000	130.000000	184.000000	109.000000	59.000000	0.000000	0.000000	176.000000	181.000000
25%	87.000000	40.000000	70.000000	141.000000	57.000000	7.000000	147.000000	33.000000	19.000000	137.000000	167.000000	318.000000	149.000000	67.000000	2.000000	5.000000	184.000000	190.250000
50%	93.000000	44.000000	80.000000	167.000000	61.000000	8.000000	157.000000	43.000000	20.000000	146.000000	179.000000	363.500000	173.500000	71.500000	6.000000	11.000000	188.000000	197.000000
75%	100.000000	49.000000	98.000000	195.000000	65.000000	10.000000	198.000000	46.000000	23.000000	159.000000	217.000000	587.000000	198.000000	75.000000	9.000000	19.000000	193.000000	201.000000
max	119.000000	59.000000	112.000000	333.000000	138.000000	55.000000	265.000000	61.000000	29.000000	188.000000	320.000000	1018.000000	268.000000	135.000000	22.000000	41.000000	206.000000	211.000000

## Check for missing values
pd.DataFrame(vehs.isnull().sum(), columns=['No. of missing values'])

	No. of missing values
compactness	0
circularity	5
distance_circularity	4
radius_ratio	6
pr.axis_aspect_ratio	2
max.length_aspect_ratio	0
scatter_ratio	1
elongatedness	1
pr.axis_rectangularity	3
max.length_rectangularity	0
scaled_variance	3
scaled_variance.1	2
scaled_radius_of_gyration	2
scaled_radius_of_gyration.1	4
skewness_about	6
skewness_about.1	1
skewness_about.2	1
hollows_ratio	0
class	0

vehs= vehs.dropna()

pd.DataFrame(vehs.isnull().sum(), columns=['No. of missing values'])

	No. of missing values
compactness	0
circularity	0
distance_circularity	0
radius_ratio	0
pr.axis_aspect_ratio	0
max.length_aspect_ratio	0
scatter_ratio	0
elongatedness	0
pr.axis_rectangularity	0
max.length_rectangularity	0
scaled_variance	0
scaled_variance.1	0
scaled_radius_of_gyration	0
scaled_radius_of_gyration.1	0
skewness_about	0
skewness_about.1	0
skewness_about.2	0
hollows_ratio	0
class	0

fig,ax = plt.subplots(figsize=(10, 10))  
numeric_cols = vehs.select_dtypes(include=[np.int64, np.float64]).columns
sns.heatmap(vehs[numeric_cols].corr(), ax=ax, annot=True, linewidths=0.05, fmt= '.2f',cmap="magma") # the color intensity is based on 
plt.show()

sns.pairplot(vehs)

<seaborn.axisgrid.PairGrid at 0x294e1ecad60>

##Check for outliers
vehs.boxplot()

<AxesSubplot:>

veh_c = vehs[numeric_cols].copy()
Q1 = veh_c.quantile(0.25)
Q3 = veh_c.quantile(0.75)
IQR = Q3 - Q1
# Replace every outlier on the lower side by the lower whisker
for i, j in zip(np.where(veh_c < Q1 - 1.5 * IQR)[0], np.where(veh_c < Q1 - 1.5 * IQR)[1]): 
    
    whisker  = Q1 - 1.5 * IQR
    veh_c.iloc[i,j] = whisker[j]
    
    
#Replace every outlier on the upper side by the upper whisker    
for i, j in zip(np.where(veh_c > Q3 + 1.5 * IQR)[0], np.where(veh_c > Q3 + 1.5 * IQR)[1]):
    
    whisker  = Q3 + 1.5 * IQR
    veh_c.iloc[i,j] = whisker[j]

veh_c.boxplot()

<AxesSubplot:>

outliers have been removed

Apply SVM

from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
X = vehs[numeric_cols].copy()
y = vehs['class']
X_train, X_test, y_train, y_test = train_test_split(X,y, random_state = 123)
from sklearn.svm import SVC
clf = make_pipeline(StandardScaler(), SVC(gamma='auto'))
clf.fit(X, y)

Pipeline(steps=[('standardscaler', StandardScaler()),
                ('svc', SVC(gamma='auto'))])

scr = clf.score(X_test, y_test)
print(f"Accuracy: {scr}")

Accuracy: 0.9656862745098039

from sklearn.metrics import plot_confusion_matrix
disp = plot_confusion_matrix(clf, X_test, y_test, cmap=plt.cm.Blues,normalize='true');
plt.grid(False)

Apply PCA

## Applying scaling using z-score
from scipy.stats import zscore
X_std = X.apply(zscore)

from sklearn.decomposition import PCA
pca = PCA().fit(X_std)
plt.plot(np.cumsum(pca.explained_variance_ratio_))

[<matplotlib.lines.Line2D at 0x294eee2d9d0>]

We see a flattening of the curve from around 7.5-9

pca = PCA(n_components=8)
X_pca = pca.fit_transform(X_std)
X_train_pca, X_test_pca, y_train_pca, y_test_pca = train_test_split(X_pca, y, random_state=123)

clf_pca =  SVC(gamma='auto')
clf_pca.fit(X_train_pca, y_train_pca)

SVC(gamma='auto')

print(f"Accuracy {clf_pca.score(X_test_pca,y_test_pca)}")
disp = plot_confusion_matrix(clf_pca, X_test_pca, y_test_pca, cmap=plt.cm.Blues,normalize='true');
plt.grid(False)

Accuracy 0.9313725490196079

The benefits of using PCA over a very large dataset usually includes

1. Reduced features, hence lower computation time
2. Standardisation of data points
3. Might improve accuracy score